{"id":"https://openalex.org/W2028042462","doi":"https://doi.org/10.1137/07068463x","title":"On the Global Solution of Linear Programs with Linear Complementarity Constraints","display_name":"On the Global Solution of Linear Programs with Linear Complementarity Constraints","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2028042462","doi":"https://doi.org/10.1137/07068463x","mag":"2028042462"},"language":"en","primary_location":{"id":"doi:10.1137/07068463x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07068463x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003645187","display_name":"Jing Hu","orcid":"https://orcid.org/0000-0001-5567-6911"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jing Hu","raw_affiliation_strings":["[email\u00a0protected] and [email\u00a0protected] and [email\u00a0protected] and [email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected] and [email\u00a0protected] and [email\u00a0protected] and [email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074563047","display_name":"John E. Mitchell","orcid":"https://orcid.org/0000-0001-5087-4679"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John E. Mitchell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002789695","display_name":"Jong\u2010Shi Pang","orcid":"https://orcid.org/0000-0002-2224-6787"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jong-Shi Pang","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048876983","display_name":"Kristin P. Bennett","orcid":"https://orcid.org/0000-0002-8782-105X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kristin P. Bennett","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049799303","display_name":"Gautam Kunapuli","orcid":"https://orcid.org/0000-0002-9297-2071"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gautam Kunapuli","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5003645187"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.7277,"has_fulltext":false,"cited_by_count":104,"citation_normalized_percentile":{"value":0.97907762,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"19","issue":"1","first_page":"445","last_page":"471"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7644385099411011},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.7435353398323059},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6885197758674622},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6502963900566101},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.6157345175743103},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5623600482940674},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.5152907371520996},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.48126524686813354},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43414077162742615},{"id":"https://openalex.org/keywords/criss-cross-algorithm","display_name":"Criss-cross algorithm","score":0.4228176474571228},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.41546663641929626},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.14477568864822388}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7644385099411011},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.7435353398323059},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6885197758674622},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6502963900566101},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.6157345175743103},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5623600482940674},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.5152907371520996},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.48126524686813354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43414077162742615},{"id":"https://openalex.org/C52486349","wikidata":"https://www.wikidata.org/wiki/Q17006040","display_name":"Criss-cross algorithm","level":4,"score":0.4228176474571228},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.41546663641929626},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.14477568864822388},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/07068463x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07068463x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.138.2877","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.2877","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.rpi.edu/~mitchj/papers/LPEC_global.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.68","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.68","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.rensselaer.edu/~mitchj/papers/LPEC_global.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4699999988079071}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W10227180","https://openalex.org/W15803339","https://openalex.org/W137768464","https://openalex.org/W217831350","https://openalex.org/W1483257570","https://openalex.org/W1501528405","https://openalex.org/W1503428021","https://openalex.org/W1508945008","https://openalex.org/W1510761797","https://openalex.org/W1563600186","https://openalex.org/W1581661059","https://openalex.org/W1588628884","https://openalex.org/W1604627832","https://openalex.org/W1720757687","https://openalex.org/W1973799058","https://openalex.org/W1976886395","https://openalex.org/W1997231674","https://openalex.org/W2000151369","https://openalex.org/W2005604902","https://openalex.org/W2013683432","https://openalex.org/W2034039293","https://openalex.org/W2037678919","https://openalex.org/W2041640046","https://openalex.org/W2042838878","https://openalex.org/W2045826029","https://openalex.org/W2047888893","https://openalex.org/W2053234120","https://openalex.org/W2054118322","https://openalex.org/W2070226140","https://openalex.org/W2070310971","https://openalex.org/W2071772344","https://openalex.org/W2074352998","https://openalex.org/W2079104779","https://openalex.org/W2079852585","https://openalex.org/W2084002138","https://openalex.org/W2086592650","https://openalex.org/W2087472326","https://openalex.org/W2102884589","https://openalex.org/W2112838397","https://openalex.org/W2124947072","https://openalex.org/W2128255043","https://openalex.org/W2133314983","https://openalex.org/W2138218159","https://openalex.org/W2138849538","https://openalex.org/W2153565720","https://openalex.org/W2155640943","https://openalex.org/W2166758048","https://openalex.org/W2171126500","https://openalex.org/W2254218369","https://openalex.org/W2608221418","https://openalex.org/W3046916097","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4205348974","https://openalex.org/W2091988699","https://openalex.org/W1979597395","https://openalex.org/W2038629892","https://openalex.org/W2040751140","https://openalex.org/W2964424355","https://openalex.org/W2081722299","https://openalex.org/W2376913782","https://openalex.org/W1520461958","https://openalex.org/W3115226252"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,12,26,94],"parameter-free":[4],"integer-programming-based":[5],"algorithm":[6,24,111,118,132],"for":[7,36,97,119],"the":[8,23,37,51,63,77,83,86,89,98,101,106,110,117,131],"global":[9],"resolution":[10],"of":[11,22,53,65,73,82,88,100,109,124],"linear":[13,16],"program":[14,29],"with":[15],"complementarity":[17],"constraints":[18,67],"(LPCCs).":[19],"The":[20,70,127],"cornerstone":[21],"is":[25,56],"minimax":[27],"integer":[28],"formulation":[30],"that":[31,130],"characterizes":[32],"and":[33,76,112,137],"provides":[34],"certificates":[35],"three":[38],"outcomes\u2014infeasibility,":[39],"unboundedness,":[40],"or":[41],"solvability\u2014of":[42],"an":[43],"LPCC.":[44],"An":[45],"extreme":[46],"point/ray":[47],"generation":[48],"scheme":[49],"in":[50,62],"spirit":[52],"Benders":[54],"decomposition":[55],"developed,":[57],"from":[58],"which":[59,91],"valid":[60],"inequalities":[61,75],"form":[64],"satisfiability":[66],"are":[68,85],"obtained.":[69],"feasibility":[71],"problem":[72],"these":[74],"carefully":[78],"guided":[79],"linear-programming":[80],"relaxations":[81],"LPCC":[84],"workhorses":[87],"algorithm,":[90],"also":[92],"employs":[93],"specialized":[95],"procedure":[96],"sparsification":[99],"satifiability":[102],"cuts.":[103],"We":[104],"establish":[105,129],"finite":[107],"termination":[108],"report":[113],"computational":[114],"results":[115,128],"using":[116],"solving":[120],"randomly":[121],"generated":[122],"LPCCs":[123,139],"reasonable":[125],"sizes.":[126],"can":[133],"handle":[134],"infeasible,":[135],"unbounded,":[136],"solvable":[138],"effectively.":[140]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}